The Math Kids: A Sequence of Events

by David Cole

  THE MATH KIDS: A SEQUENCE OF EVENTS

  Published by Common Deer Press Incorporated.

  Text Copyright © 2019 David Cole

  Illustration Copyright © 2019 Shannon O’Toole

  All rights reserved under International and Pan-American Copyright Conventions. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without permission in writing from the publisher, except by a reviewer, who may quote brief passages in a review.

  Published in 2018 by Common Deer Press

  3203-1 Scott St.

  Toronto, ON

  M5V 1A1

  This book is a work of fiction. Names, characters, places, and incidents are either the product of the author’s imagination or are used fictitiously.

  Library of Congress Cataloging-in-Publication Data

  Cole, David.-First edition.

  The Math Kids: A Sequence of Events / David Cole

  ISBN: 978-1-988761-30-5 (print)

  ISBN: 978-1-988761-31-2 (e-book)

  Cover Image: © Shannon O’Toole

  Book Design: Ellie Sipila

  Printed in Canada

  WWW.COMMONDEERPRESS.COM

  FOR MARY ANNE, WHO ALWAYS MADE SURE I HAD PLENTY OF BOOKS TO READ.

  CHAPTER 1

  Ironically, it had all started with a math puzzle. The next thing I knew, the newest member of our math club had disappeared.

  After three days without a sign of her, we decided it was time for the Math Kids to do something about it.

  But I’m getting ahead of myself, so I’ll begin at the beginning…

  It was Friday, and we had almost made it through another week with Mrs. Gouche. She was our fourth-grade teacher and wasn’t too bad most of the time. I liked that she had separate math groups, so we didn’t get stuck doing the easy math with Robbie Colson and Sniffy Brown.

  Sniffy’s real name is Brian, but everyone calls him Sniffy because he always has a runny nose and sniffs loudly. We never call him Sniffy to his face, of course. He is friends with Robbie, Bill Cape, and Bryce Bookerman, the class bullies.

  “Don’t forget that we have Math Kids club tomorrow,” I reminded Stephanie on the way into class. I’m the president of the Math Kids club at McNair Elementary School. I hadn’t exactly been elected to the position, though. Stephanie Lewis had said I should be president since the club was my idea, and Justin Grant, my best friend since kindergarten, hadn’t objected. There was no need for an election because there were only three of us in the club.

  I already knew Justin was coming to the meeting because we had talked about possible problems to tackle while we walked to school that morning. Justin had a new book of math puzzles he was planning to bring.

  You’re probably thinking that all we do in the Math Kids club is sit around and solve math problems. That was how the club had started, but it sure took a few strange turns along the way. Who would have thought we could use math to crack a case the police couldn’t solve? Still, the original idea for the club was to solve math problems. And when all the excitement with the burglars was over, trust me, that’s all we wanted to do.

  “Wouldn’t miss it, Jordan!” Stephanie said. “No, wait! I have soccer practice, so it would have to be after that.”

  I rolled my eyes as I took my seat in class. This would take some finessing on my part. Justin and Stephanie had had more than one blowup over her soccer practices colliding with our math club. But finding a way to avoid another shouting match was a problem I’d face after school.

  Mrs. Gouche has been giving our math group tougher and tougher problems as the school year goes on. She knows that Stephanie, Justin, and I are good at math and really like hard problems, so she has made it her mission to really challenge us. This day’s problem, for example, was no exception.

  “This, my friends, is called The Sixes Problem. Catherine, can you hand this to Jordan?”

  The girl who sat in front of me—Catherine…something—handed me the problem sheet. I noticed she took a long look at it before passing it back to me. I smiled, knowing that she probably wouldn’t have the first clue about how to solve the kind of problems our teacher had been giving us. Little did I know that she actually knew a lot more than I thought and would end up being right in the middle of our next mystery.

  Mrs. Gouche put her dry-erase marker down and returned to her desk. She had an evil glint in her eye and my heart started to beat a little faster.

  The problem looked simple enough when I first scanned it. We had to use three of the same number, like 2, 2, 2 or 5, 5, 5, and any mathematical operations, like multiplication, division, or addition, to make 6. For example, to solve for the number 2 we could use 2 × 2 + 2 = 6. It didn’t look difficult, but it turned out to be much tougher than we thought!

  We went to the whiteboard and started working. We easily came up with answers for the numbers 2 and 6:

  2 × 2 + 2 = 6

  6 + 6 – 6 = 6

  The problem was that we had to do the same thing with all the numbers from 0 to 9.

  While the rest of the class was working on their social studies homework, the three of us stood at the whiteboard, dry-erase markers in our hands, as we tried to solve for all the numbers.

  Justin got us the next two answers when he remembered that any number divided by itself is just one.

  That means that 5 ÷ 5 is just 1 so we could use 5 + 5 ÷ 5 = 6. We used the same trick to solve for the number 7.

  That meant we had four down and six to go:

  2 + 2 + 2 = 6

  5 + 5 ÷ 5 = 6

  6 + 6 − 6 = 6

  7 − 7 ÷ 7 = 6

  Zero and 1 looked impossible. We thought they might really be impossible, too. We had lost a class pizza party when Stephanie bet Mrs. Gouche that we would solve a problem called the Bridges of Königsberg. It turned out that the problem didn’t have an answer. Score one for Mrs. Gouche!

  “I don’t think there are answers for zero and one,” Justin complained.

  “Me neither,” I added. “Let’s work on three and four. I’m sure we can get those.”

  Three turned out to be pretty easy: (3 x 3) – 3 = 6. We were halfway there!

  And halfway there was as far as we got. We stared at the board and made some attempts at new ideas, but the last five answers remained out of our reach. The three o’clock dismissal bell rang while we were still staring at the board.

  “We did pretty well, Mrs. Gouche,” I announced. “We’ve only got three more to go.”

  She glanced up at the board.

  “It looks like five more to go, Mr. Waters. Did you forget about zero and one?” she asked, turning her focus back to the papers she was grading.

  “But those are impossible,” I protested. “You were trying to trick us again.”

  “No tricks this time,” she said. “There are answers for every number from zero to nine.”

  We stared at the remaining problems on the board. There was no way we could do anything to get three 1s to somehow equal 6. And the 0s? Forget about it.

  The class started to gather up their papers and books and stuff them into backpacks. Robbie and his buddies pushed each other as they rushed to get out of the room. None of the bullies had detention for a change, so they were anxious to get out to the playground for a game of soccer.

  We were on temporary good terms with the bullies. I wasn’t sure how long it would last, but at least, for the moment, I didn’t have to worry about them knocking my backpack to the floor, or tripping me as I walked past them, or threatening to rearrange my face at recess. We had Stephanie to thank for that. It had been her idea to have Robbie�
��s dad help us catch the burglars. Mr. Colson is a police officer, but usually doesn’t do anything more exciting than writing parking tickets. When we used our math skills to figure out when and where the burglars were going to hit next, Stephanie had found a way for Mr. Colson to get credit for cracking the case. Robbie’s dad was happy, which meant we were on Robbie’s good side—temporarily anyway.

  “Well, I guess I know what we’ll be working on in the Math Kids club tomorrow,” I said with a frown. Normally, I would have been happy to work on a tough math problem, but I knew there was no way we were going to be able to solve this one.

  “Let’s start early tomorrow,” Justin said. “We could meet at—”

  “I’ve got soccer practice,” Stephanie interrupted.

  “Of course you do,” Justin replied sarcastically. “The sun is up, so you must have soccer practice.”

  Stephanie gave him an irritated look as she tugged on her ponytail. Wanting to avoid an argument, I jumped in quickly.

  “How about Justin and I get started and you come over after practice?” I asked.

  “Yeah, that would work,” she said.

  “It doesn’t really matter,” Justin sulked. “We’re never going to get answers for zero and one anyway.”

  “Factorials,” said a small voice near the door.

  “What did you say?” asked Justin.

  “Factorials,” repeated the small voice, which we could now see had come out of the mouth of the girl who sat in front of me, Catherine…Duchesne. I knew I’d remember her last name eventually. “You need to use factorials to solve for zero and one.”

  “How is a factory going to help us solve a math problem?” I asked.

  “Not a factory,” she said, laughing. “Factorials.”

  And with that, she was out of the room and disappeared into the crowd of students headed down the hallway to the exits.

  CHAPTER 2

  I was halfway through my second bowl of cereal on Saturday morning when Justin called.

  “Come on, we’re going to practice,” he said without even a hello.

  “Practice what?”

  “Soccer.”

  You could have knocked me over with a feather. Justin was not the most athletic kid. The only sport he kind of liked was basketball, which was kind of funny since he was the shortest kid in the class.

  “Why are we going to practice soccer?” I asked.

  “We’re not. We’re doing math,” he replied. “I’ll meet you out in front of your house in ten minutes.”

  I was completely confused, but I scarfed down the rest of my cereal and grabbed the pair of sneakers I had left by the front door. I was lacing them up on my front porch when Justin appeared. He was wearing his backpack, which looked even more stuffed than usual.

  “Let’s go,” he called. “Time’s a wasting.”

  I finished tying my shoes and followed Justin, who was already on his way down the street.

  “Care to explain what we’re doing?” I asked.

  “It’s simple. If we can’t get Stephanie to come to math club in the morning because of her stupid soccer practice, we’ll take the math club to her.”

  We got to the soccer park fifteen minutes later. There were six soccer fields filled with kids of all ages. It took a little while to find Stephanie’s field, but we finally saw her doing a dribbling drill with her teammates. While I watched her practice (she was amazing—by far the fastest girl on her team and she handled the ball like it was on a string), Justin dug into his backpack. He pulled out a portable easel and extended the legs. Next came a mini whiteboard, then a set of colored markers. Finally, he pulled out a roll of cellophane tape and The Sixes Problem with our previous answers filled in. He taped the paper to the bottom of the whiteboard.

  “There you go,” he said with satisfaction. “A portable classroom.”

  The look on his face was so serious that I had to laugh. He looked crestfallen for a moment, then broke into his own grin.

  “That’s pretty low-tech for you, isn’t it?” I asked, knowing that Justin loved computers and spent hours every day playing fast-paced video games.

  “I couldn’t find an extension cord long enough to make it to the soccer field.” Justin smiled at his own joke.

  “So how is Stephanie going to play soccer and do math at the same time?” I asked.

  “They have to give her a break every once in a while, don’t they?”

  “Yeah, I guess.”

  “Well, she can do math while she rests.”

  Justin’s plan ended up working very well. It turned out Stephanie could do fancy footwork and fancy brainwork at the same time. As she practiced throw-ins from the sideline, she called over to Justin.

  “Can we use square roots?” she asked.

  Her coach wasn’t happy about the distraction, but her suggestion was genius.

  A square root of a number is a value that, when multiplied by itself, gives the number. The square root of 4 (written as √4) is 2, for example, since 2 × 2 = 4. The square root of 9 is 3, since 3 × 3 = 9.

  As soon as Stephanie got the words “square roots” out of her mouth, Justin was already writing an answer for the number 4 on the mini whiteboard:

  √4 + √4 + √4 = 6

  Since √4 = 2, it was just like saying 2 + 2 + 2 = 6.

  I got the next one myself:

  (9 + 9) ÷ √9 = 6

  Justin turned his head to one side as he squinted at my answer. I knew that look, so I explained it to him.

  “Nine plus nine equals eighteen and the square root of nine is three,” I explained.

  “So, it’s just eighteen divided by three,” he finished.

  “Nice work, Stephanie!” I called out. “We got two more!”

  She smiled and gave me a high five as she ran past. “Nice job, guys!” she shouted, earning another look of disapproval from her coach. A short time later, it was the coach giving Stephanie a high five as she found the upper corner of the goal with a difficult left-footed shot.

  Justin solved the toughest part of The Sixes Problem yet when he came up with a solution using three 8s while Stephanie was on a water break. She and I had to stare at his answer for some time before we finally got it:

  8 − √(√(8 + 8)) = 6

  Stephanie talked it out as she tried to figure out what Justin had done.

  “So, eight plus eight equals sixteen,” she started. “Then you take the square root of sixteen to get four.”

  That’s when I got it.

  “And then you take the square root of four to get two,” I added, pointing at the second square root symbol.

  “And eight minus two equals six,” finished Justin. He was trying not to smile, but I could tell he was very proud of what he had come up with.

  “That’s brilliant!” shouted Stephanie, drawing another stern look from her coach.

  “You want to get back in the game?” he called over.

  “Gotta go. We should be done in a few minutes, though,” she said as she hustled back out on the field. “See you back at your house, Justin.”

  Justin packed up his portable classroom. We had solved all but 0 and 1, which I was pretty sure were impossible, despite what Mrs. Gouche had told us.

  2 + 2 + 2 = 6

  (3 x 3) – 3 = 6

  √4 + √4 + √4 = 6

  5 + 5 ÷ 5 = 6

  6 + 6 − 6 = 6

  7 − 7 ÷ 7 = 6

  8 - √(√(8 + 8)) = 6

  (9 + 9) ÷ √9 = 6

  A short while later, back at Justin’s house, Stephanie started the official Math Kids meeting with two questions.

  “Who was that girl yesterday and what is a factorial?”

  I could answer the first question. I was hoping Justin could answer the second.

  “Her name is Catherine Duchesne,” I told Stephanie. “She sits in front of me.”

  “Does she know anything about math?” she asked.

  “How should I know?” I said. “I don’t think
I’ve ever even heard her speak before. I think she’s in the red math group.”

  The math groups in our room were all named after colors. We were in the yellow group. After that came blue, then red, and then finally green: the group that Robbie and Sniffy and the rest of the bullies were in.

  “How can someone in the red group know so much about math?” Stephanie asked. “I don’t think that’s possible.”

  “Well, in this case, it’s definitely possible,” Justin chimed in.

  Stephanie and I looked at him.

  “I asked my dad about factorials last night, and I think Catherine may be right,” Justin said.

  “Are you kidding me?” I asked in surprise. “She’s in the red group. That’s just one group ahead of Robbie and his bully friends. They can’t count past ten because they run out of fingers.”

  “Before we get into how she knew about it, can you explain what it is we’re talking about?” Stephanie asked.

  Justin went on to explain factorials, which were pretty easy to understand. A factorial is written with an exclamation point after the number and all it means is to multiply the number by all the numbers less than it. So, 4! = 4 × 3 × 2 × 1 = 24.

  That looks like it could really be the answer! We knew it was when we figured out that 3! = 3 × 2 × 1, which is equal to 6. Boom, there was the answer for using three 1s to get to 6! We just had to get to 3 and use a factorial. And to get to 3, all we had to do was add the three 1s:

  (1 + 1 + 1)! = 3! = 6

  High fives all around. Catherine was right! Factorials were the answer.

  “That’s great for the ones, but how is that going to work for zeroes?” I asked. “Zero factorial is just going to be zero again, so we’re still stuck.”

  Stephanie and I were discouraged, but Justin had a big smile on his face.

  “Spill it,” I said.

  “Spill what?” he asked innocently.

  “You know exactly what I’m talking about. You know something you’re not telling us.”

  “Me? I don’t know anything,” Justin said, but I could tell he did.

  “No cookies for you unless you tell us what you know.”